Introduction to bifurcation theory

Introduction to bifurcation theory

The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail:...

An introduction to bifurcation theory

The aim of this chapter is to introduce tools from bifurcation theory which will be necessary in the following sections for the study of neural field equations (NFE) set in the primary visual cortex. In a first step, we deal with elementary bifurcations in low dimensions such as saddle-node, transcritical, pitchfork and Hopf bifurcations. NFEs are dynamical systems defined on Banach spaces and ...

PhD mini course: introduction to bifurcation analysis

This pdf document provides the textual background in the mini course on bifurcation analysis, by George van Voorn. It is the companion material by the powerpoint presentations posted on the site www.bio.vu.nl/thb. Goal of this manuscript is to explain some of the basics of bifurcation theory to PhD-students at the group. The emphasis is strongly on the biological interpretation of bifurcations;...

Introduction to Model theory

These notes aim at giving the basic definitions and results from model theory. My intention in writing them, is that they should provide the reader with many examples, even with some proofs, and contain most of the definitions. Differences in vocabulary can be quite an obstacle to mutual understanding, and having the terminology written up somewhere should prove helpful. An index is included at...

Introduction to Queueing Theory